L12 Glazer and Rubinstein ECMA 2004 Information Transmission in Markets SR setting with type independent preferences of S Benchmarks Cheap Talk only bubbling equilibrium Perfectly ID: 626164
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Slide1
Partly Verifiable Signals
L12
Glazer and Rubinstein (ECMA 2004) Slide2
Information Transmission in Markets
S-R setting with type independent preferences of S
Benchmarks: - Cheap Talk (only bubbling equilibrium) - Perfectly (costlessly) verifiable types (only fully revealing equilibrum)Realistic Settings: fact checking is costly and verification is partialQuestions: - Uncertainty about verifiability - Which party should verify information? - Optimal verification effort? - Does prior communication improve verification process? - If yes, what is the optimal verification mechanism?Slide3
Partial verification
State space where is an aspect and quality is
Uncertainty about verification (Shin 2003)Low types S strategically withhold negative informationPooling at the bottomUncertainty mutes R’s skepticismresult in asymmetric return dynamicsUnaware buyers (Milgrom and Roberts 1986)R unaware which characteristics are relevantS announce high but irrelevant test scoresTest scores ignored by RWith heterogenous buyers competition among S better than regulationSlide4
Costly verification
Costly verification by a sender (
Jovanovic 1982)Excessive testing and selective reporting (data mining) Welfare loss (as in the signaling literature) Costly verification by a receiver (Townsend 1979)Insurance against wealth shocksS informs about the wealth shock R can verify the claim at some costOptimal contract: no verification until defaultToday: capacity constraint (can verify only one aspect)Slide5
Motivating example
A candidate with two characteristics (talent, loyalty) and an employer
Decision: hire, not hireCandidate (sender, speaker) - strictly prefers action ``hire’’ - can send a message regarding his characteristicsEmployer (receiver, listener) - wants to hire only if sum of characteristics above one - has capacity to verify only one characteristicQuestions:Can employer reduce probability of a mistake by talking to a candidate?If yes, how should he verify information obtained in the conversation?Slide6
Glazer and Rubinstein persuasion game
State space with aspect
Action space Sender always prefers Acceptance and rejection region Verification mechanism Slide7
Preferences over Verification Mechanism
Fix
Let R preferences over verification mechanisms Type one error Type two error mechanism is R-optimal if it solvesRemarks: We search for the best verification mechanism for RCommitment (this assumption is relaxed)More general loss function and arbitrary prior Slide8
Important classes of Mechanisms
Direct mechanism
Deterministic mechanismBubbling mechanism Slide9
Does conversation improve welfare?
Consider candidate-employer problem
Bubbling mechanism improves over no verificationConversation improves over a ``bubbling’’ mechanismSlide10
L-principle
Assume
Consider any three types forming ``L’’ P: For any mechanism the sum of mistake probabilities is``Mass of independent ``Ls’’ gives a lower bound for the number of mistakesEasy check of mechanism optimalitySlide11
Proof: L-principle
Fix mechanism and . Let be optimal for